If 2 cards are drawn from a well shuffled pack of 52 cards, the probability that they are of the same colour is:

Concept:

• The probability of drawing ‘k objects of type p’ from a collection of n = p + q + r + … objects, is given by: \(\rm P =\dfrac{^{p}C_{k}}{^{n}C_{k}}\).

• Probability of a Compound Event [(A and B) or (B and C)] is calculated as:

  P[(A and B) or (B and C)] = [P(A) × P(B)] + [P(C) × P(D)]

  ('and' means '×' and 'or' means '+')

Calculation:

There are 26 red and 26 black cards in a pack of 52 cards.

∴ The probability of drawing 2 cards of the same color can be written as:

= P(Both cards are red) OR P(Both cards are black)

\(\rm =\dfrac{^{26}C_{2}}{^{52}C_{2}}+\dfrac{^{26}C_{2}}{^{52}C_{2}}\)

\(\rm =\dfrac{\dfrac{26\times25}{2}}{\dfrac{52\times51}{2}}\times2\)

\(\rm =\dfrac{26\times25}{52\times51}\times2=\dfrac{25}{51}\)